Dynamic Water Quality Model

The InfoWorks WS Pro Dynamic Water Quality Model is based on EPANET concepts and numerical procedures as described in the EPANET 2.0 Users Manual, Appendix D.2.

The Dynamic Water Quality Model tracks the fate of a dissolved substance flowing through the network over time. It uses the flows from the hydraulic simulation to solve a conservation of mass equation for the substance within each link connecting nodes i and j:

(1) where:  cij= concentration of substance in link i,j as a function of distance and time (for instance, cij = cij(xij,t)), mass/m3 xij = distance along link i,j, m qij = flow rate in link i,j at time t, m3/s Aij = cross-sectional area of link i,j, m2 q(cij) = rate of reaction of constituent within link i,j, mass/m3/day

 

Equation (1) must be solved with a known initial condition at time zero and the following boundary condition at the beginning of the link, that is, at node i where xij = 0:

(2)

The summations are made over all links k,i that have flow into the head node (i) of link i,j, while Lki is the length of link k, Mi is the substance mass introduced by any external source at node i, and Qsi is the source flow rate. The boundary condition for link i,j depends on the end node concentrations of all links k,i that deliver flow to link i,j, thus Equations (1) and (2) form a coupled set of differential/algebraic equations over all links in the network.

Eulerian transport model - Discrete Volume Element Method

By default, InfoWorks WS uses a numerical scheme called the Discrete Volume Element Method (DVEM) to solve the above equations. DVEM is an Eulerian method (implemented in EPANET v1.1) which divides a pipe into completely mixed volume segments and models the transport between the elements.

Within each hydraulic time period when flows are constant, DVEM uses a shorter water quality time step and divides each pipe into a number of completely mixed volume segments. Within each water quality time step, the material contained in each pipe segment is first reacted. Then at each node the concentration is computed from the mixture of the mass and flow entering that node from adjacent segments in each connected pipe. The mass within each pipe segment is then transferred to its adjacent downstream segment. After this transport step is completed for all pipes, the previously calculated concentration at each node is released into the head end segments of pipes with flow leaving the node. This sequence of steps is repeated until the time when a new hydraulic condition occurs. After obtaining the new hydraulic solution the network is then re-segmented and the water quality computations are continued.

The water quality time step used in the method can be chosen by the user. The default value is one tenth of the hydraulic time step. In either case the value chosen should be as large as possible without causing the flow volume of any pipe to exceed its physical volume (that is, have mass transported beyond the end of the pipe). Thus the water quality time step dtwq should not be larger than the shortest time of travel through any pipe in the network, that is:

(3) where: Vij = volume of pipe i,j qij = flow rate of pipe i,j

With this water quality time step, the number of volume segments in each pipe (nij) is:

(4) where: INT[x] = largest integer less than or equal to x

The program limits nij to be no smaller than 1 and no greater than 1000. If dtwq is found to be greater than the above limit a warning is written to the simulation log file.

Lagrangian transport model

By default, InfoWorks WS uses the Discrete Volume Element Method (DVEM) to model transport.

The Time Driven Method (TDM) is a Lagrangian method (implemented in EPANET v2.0) which can be used instead of the DVEM by setting the Use Lagrangian Solver check box in the Water Quality Options dialog.

The TDM tracks the movement of segments of water as they move through pipes in the network and mix together at nodes. As the simulation progresses, the size of the most upstream segment in the pipe increases as water enters the pipe, while the most downstream segment decreases in size as water leaves the pipe. The size of the segments in between remains unchanged.

The initial number of segments in each pipe is calculated by using equations (3) and (4) above.

For each water quality time step the following steps are carried out:

1. Reactions in each segment are calculated and water quality updated
2. Water flowing into each junction is blended together to calculate a new water quality value at the junction.
3. New segments are created in pipes with flow out of each node, where the segment volume is: pipe flow multiplied by water quality time step.

Note: new segments are only created if the difference between quality at the node and the quality of the last segment in the outflow pipe is greater than the age, concentration or trace percentage tolerance values specified on the Water Quality Options dialog. If the difference in quality is below the tolerances specified, the size of the existing segment is increased instead of creating a new segment.

Reaction rate model

See Reaction rate model.

MSQ model

See MSQ model.

Water age and source tracing

In addition to chemical transport, the water quality model calculates the changes in age of water over time throughout a network. To accomplish this, the program interprets the variable c in Equation (1) as the age of water and sets the reaction term q(c) in the equation to a constant value of 1.0. During the simulation, any new water entering the network from fixed heads, wells or transfer nodes enters with the specified initial age. Water age provides a simple, non-specific measure of the overall quality of delivered drinking water. When the model is run under constant hydraulic conditions, the age of water at any node in the network can also be interpreted as the time of travel to the node.

The water quality model can also track over time what percentage of water reaching any node in the network had its origin at a particular node. In this case the variable c in Equation (1) becomes the percentage of flow from the node in question and the reaction term is set to zero. The value of c at the source node is kept at 100 percent throughout the duration of the simulation. The source node can be any node in the network, including storage nodes. Source tracing is a useful tool for analysing distribution systems drawing water from two or more different raw water supplies. It can show to what degree water from a given source blends with that from other sources, and how the spatial pattern of this blending changes over time.

InfoWorks WS Pro can trace water from up to ten nodes simultaneously. It should be noted that when there is more than one trace node, if the positions of these nodes are not selected carefully, it may be possible for water from one trace node to reach another. If this occurs, at the downstream trace node, the percentage of water from that trace node will still be 100 percent, but a certain percentage of that will have come from the upstream trace node. That is, at any node, the reported percentages of water arriving from each trace node are individually correct. However, if water from one trace node is also made up of water from another, the individual percentages should not be expected to sum to 100 percent. If this mixing occurs, a warning will be written to the simulation log file identifying the two trace nodes involved. In this case, either the trace node percentage will require careful interpretation, or the location of those trace nodes should be reconsidered and the simulation rerun.